In triangle abc, angle c is 90 degrees, bc = 2, sin B = root of 3 divided by 2. find AB

Since SinABS = √3 / 2, then the angle ABC = 600, then the angle BAC = (90 – 60) = 30.
The BC leg, which lies opposite the angle of 300, is two times shorter than the hypotenuse AB.
Then AB = 2 * BC = 2 * 2 = 4 cm.
In a right-angled triangle ABC through the sine of the angle ABC, we define the cosine of this angle.
Cos2ABC = 1 – Sin2ABC = 1 – (√3 / 2) 2 = 1 – 3/4 = 1/4.
CosABC = 1/2.
Through the cosine ABC of the angle and the adjacent leg BC, we determine the length of the hypotenuse AB.
CosABS = BC / AB.
AB = BC / CosABC = 2 / (1/2) = 2 * 2/1 = 4 cm.
Answer: The length of the hypotenuse AB is 4 cm.